$A$ quantity $z$, to be estimated, has a dependency on the variables $a, b$ and $c$ as $z = a b^2 c^{-2}$. The percentage errors in the measurement of $a, b$ and $c$ are $2.1 \%$, $1.3 \%$ and $2.2 \%$, respectively. The percentage error in the measurement of $z$ would then be: (in $\%$)

An artificial satellite is revolving around a planet of mass $M$ and radius $R$ in a circular orbit of radius $r$. From Kepler's third law about the period of a satellite around a common central body,the square of the period of revolution $T$ is proportional to the cube of the radius of the orbit $r$. Show using dimensional analysis that $T = \frac{k}{R}\sqrt{\frac{r^3}{g}}$,where $k$ is a dimensionless constant and $g$ is the acceleration due to gravity.

If $L$,$C$,and $R$ denote the inductance,capacitance,and resistance respectively,the dimensional formula for $C^{2}LR$ is

If momentum $(P)$,area $(A)$,and time $(T)$ are taken to be fundamental quantities,then energy has the dimensional formula of:

The dimensions of the product $\mu_{0} \varepsilon_{0}$ are related to those of velocity as

Consider the equation $H = \frac{x^p \epsilon^q E^r}{t^s}$, where $H = \text{magnetic field}$, $E = \text{electric field}$, $\epsilon = \text{permittivity}$, $x = \text{distance}$, and $t = \text{time}$. The values of $p, q, r$, and $s$ respectively are: